Logical Reasoning

PT103 · S2 · Q16 Every new play that runs for more

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Every new play that runs for more than three months is either a commercial or a critical success.

Conclusion (Therefore)

Every new play that ran for more than three months last year was a commercial success.

Evidence

Every new play that runs for more than three months is either a commercial or a critical success.

Last year, all new plays that were critical successes were also commercial successes.

Evaluate

Since this argument has some conditional logic (every, all, every) and repeating language in it, we should probably look at the algebraic recipe of the logic. We know that all three ingredients are conditionals, so any answer that doesn't have three conditional ingredients should be wrong.

P1: Every new play that runs A + X → B or C 3+ mos is comm or crit succ

P2: All new plays that were A + C → B crit succ were comm succ

C: Every new play that runs A + X → B 3+ mos is comm succ

The algebra here is tricky since all three claims are about "new plays", but a specific subset of "new plays".

One premise and the conclusion are about "New plays that run for 3+ months". The other premise is about "New plays that are critical successes".

It might be easier to think about this one conversationally.

P1: If you're A, then you're B or C P2: But if you're C, then you're also B. C: So if you're A, you're destined to be B.

Goal

Look for a conditional premise that offers us some "B or C" in the outcome. Then look for a second conditional premise that makes it seem like "one of those two options implies the other". Thus, you're bound to be the implied option either way.

16.

The pattern of reasoning in which one of the following arguments is most similar to that in the argument above?

  1. Most new restaurants require either

    Bad Premise Match: no conditionals

    We can tell from a bird's eye view that we're not getting three conditionals here: Most, Most, Guaranteed. Without the conditionals, it's not going to be a strong enough match.

    7% picked this

  2. Every best-selling cookbook published last

    Bad Premise Match: just 1 conditional

    We can tell from a bird's eye view that we're not getting three conditionals here. The first claim is a conditional, but then the 2nd premise and the conclusion are both just facts. Without the conditionals, it's not going to be a strong enough match.

    8% picked this

  3. Correct

    All students at the Freeman

    Why this is right

    We wanted a conditional premise that offers us some "B or C" in the outcome. 2nd yr Student at FSC ? dessert or soup Then look for a second conditional premise that makes it seem like "one of those two options implies the other". study soup ? study dessert Thus, you're bound to be the implied option either way. 2nd yr Student at FSC ? dessert We could still use our gross algebraic recipe too if we wanted / needed to. A + X ? B or C A + C ? B A + X ? B A = student at Freeman X = 2nd year B = study desserts C = study soups

    Skill tested: Parallel · how this choice captures the argument's function is the move to repeat next time.

    84% picked this

  4. Chefs who become celebrities either

    Bad Premise Match: just 1 conditional

    We can tell from a bird's eye view that we're not getting three conditionals here. The first claim is a conditional, but then the 2nd premise and the conclusion are both just facts. Without the conditionals, it's not going to be a strong enough match. We also could have rejected this as soon as we saw the "but not both" attached to our either/or outcome. The way this argument works is that the 2nd premise is supposed to be saying, "If you're one of these two options, you're also the other", so there needs to be a possibility of being both options in order to match the original argument.

    1% picked this

  5. Every catering service in Woodside

    Bad Premise Match: just 1 conditional

    We can tell from a bird's eye view that we're not getting three conditionals here. The first claim is a conditional, but then the 2nd premise and the conclusion are both just facts. Without the conditionals, it's not going to be a strong enough match. We could also reject this as soon as we see that the first conditional has an "and" outcome. We needed an "or" outcome.

    1% picked this

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